Chapter3 Image Enhancement in the Spatial Domain

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Chapter3Image Enhancement in the Spatial Domain

• 3.0 Introduction
• 3.1 Background
• 3.2 Some Basic Gray Level Transformations
• 3.3 Histogram Processing
• 3.4 Enhancement Using Arimethic/Logic Operations
• 3.5 Basics of Spatial Filtering
• 3.6 Smoothing Spatial Filters
• 3.7 Sharpening Spatial Filters
• 3.8 Combining Spatial Enhancement Methods

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3.0 INTRODUCTION

• 1. Objective
• to process an image so that the result is more
  suitable for specific applications.
• 2. Categories
• a. spatial domain methods.
• b. frequency domain methods.
• c. combinations of above two types.

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3.1 BACKGROUND

• 1. Operate directly on an image f by the
  following way
• g(x, y) T f (x, y)
• where g is the processed image and T is an
  operator over an n ? n neighborhood of f
• For simplicity in notation
• S T(r)
• r and s is the gray level of f(x,y)and g(x,y)

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3.1 BACKGROUND
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3.1 BACKGROUND

• 2. Point processing -- for n 1, i.e.,
• neighborhood the pixel itself
• 3. Mask processing -- also called filtering
• for n ? 1 neighborhood n ? n pixels using
  masks.

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4.2 ENHANCEMENT BY POINT PROCESSING

• 4.2.1 Some Simple Intensity Transformations
• 4.2.2 Histogram Processing
• 4.2.3 Image Subtraction
• 4.2.4 Image Averaging

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4.2.1 Some Simple Intensity Transformations(1)

• 1. Image negatives
• given a pixel gray level ( g. l. ) r, output
  pixel g. l. s is

L-1
T
s
L-1 largest g. l.
r
L-1
0
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4.2.1 Some Simple Intensity Transformations(2)

• 2. Contrast stretching
• (1) Stretching is useful for improving image
  contrast.
• (2) General transformation diagram.

L-1 largest g. l.
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4.2.1 Some Simple Intensity Transformations(3)

• (3) cases
• a. no change -- if r1 s1 , r2 s2 .
• b. thresholding -- if r1 r2, s1 0, and s2
  L-1
• threshod value r1 r2.
• c. stretching -- if r1? r2 s1? s2 ( to keep
  monotonicity of transformation )
• d. Why dies stretching improve image contrast?
• e. How to stretch is problem - dependent

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4.2.1 Some Simple Intensity Transformations(4)
Mappings AgtT(A) (longer gt smaller)
L-1 largest g. l.
B gt T(B) (smaller gt larger ) CONTRAST IMPROVED)
C gt T(C) (larger gt smaller)
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4.2.1 Some Simple Intensity Transformations(5)

• 3. Compression of dynamic ranges
• (1) Gray levels may be out of the display range
  after certain transformations.
• (2) One way to compress is
• S T( r ) c log(1 r )
• where c is a constant to make s to lie between 0
  and L-1

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4.2.1 Some Simple Intensity Transformations(6)

• 4. Gray level slicing
• (1) Highlighting a specific g. l. range
• (2) Useful for many applications.
• (3) Two approaches
• a. use high values for desired ranges and low
  values for others
• b. use high values for desired ranges and keep
  the values for others.
• (4) See Fig 4.7

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Fig 4.7
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4.2.1 Some Simple Intensity Transformations(7)

• 5. Bit-plane slicing
• (1) Highlighting contributions made by specific
  bits to image appearance.
• (2) More important information is included in
  higher- order bit planes details in others (see
  Fig. 4.8 )
• (3) Bit - plane 7 ( highest - order ) result
  of thresholding with threshold 128
• (4) See Fig. 4.9

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4.2.2Histogram Processing(1)

• 1. Definition and properties of histogram
• (1) the histogram of a given image f is a
  function
• P( rk ) nk / n
• where rk the kth g. l.
• nk the no. of pixels with g.l. rk
• n the total no. of pixels in f.
• (2) Diagram of histogram

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4.2.2Histogram Processing(2)

• (3) Concept
• histogram p.d.f ( probability density
  function )
• (4) A histogram gives the global appearance of an
  image .
• (5) Histograms of images with high and low
  contrasts (see Fig. 4.10 )

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4.2.2Histogram Processing(3)

• 2. Histogram equalization
• (1) Equalization transformation of a given image
  f
• where Pr(w) is the histogram of f
• (2) S above is exactly the c. d. f. of r ( c. d.
  f. cumulative distribution function )

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4.2.2Histogram Processing(4)

• (3) It can be shown by probability theory (see
  textbook) that the new image with g. l. s has a
  uniform distribution, i.e.,
• (4) the transformation illustration

Pr(r)
Ps(s)
Equalization
r
S
Image with low contrast
Image with higher contrast
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4.2.2Histogram Processing(5)

• (5) Read the example in pp. 176-177.
• (6) Histogram equalization is also called
  histogram flatting or linearization.
• (7) Discrete form of histogram equalization

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4.2.2Histogram Processing(6)

• (8) A computation example

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4.2.2Histogram Processing(7)

• (9) A major advantage of histogram equalization
  for image contrast enhancement is that it can be
  applied automatically.
• (10) See Fig. 4.14 for a real example.
• 3. Histogram specification
• See textbook
• 4. Local enhancement
• See textbook

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4.2.3Image Subtraction

• 1. Computes the difference g of two images f and
  h
• 2. For application example, see Fig. 4.17

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4.2.4Image Averaging

• 1. Reduces noise by averaging several copies of
  and identical image
• 2. Method
• where gi(x, y) is one of copies of origin image
• 3. Why work ? Noise standard deviation can be
  reduced to 1/n of origin
• 4. See Fig. 4.18

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4.3Spatial Filtering

• 4.3.1 Background
• 4.3.2 Smoothing Filtering
• 4.3.3 Sharpening Filtering

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4.3.1 Background(1)

• 1. Spatial filtering is also called mask
  processing.
• 2. Masks ( also called spatial filters ) are used
• 3. High - frequency components in images
• noise, edges, sharp details, etc.
• 4. Low - frequency components in images
• uniform regions, slow - changing background g.
  l., etc.
• 5. Type of spatial filtering
• (1) lowpass filtering
• useful for image blurring (smoothing)

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4.3.1 Background(2)

• (2) Highpass filtering
• useful for image sharpening
• (3) Bandpass filtering
• mostly used in image restoration
• 6. See Fig 4.19 for the above 3 types.
• 7. Linear mask operation

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4.3.1 Background(2)

• Operation replace z5 by
• R M?N z1?w1 z2?w2 . z9?w9
• 8. Nonlinear mask operation
• R is computed nonlinearly using information of
  the neighborhood of current pixel as well as the
  mask.

Z5 g. l. of current pixel
Mask M
Neighborhood N
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4.3.2Smoothing Filters(1)

• 1. Used for image blurring noise reduction.
• 2. Useful for removing small details and bridging
  small gaps in lines or curves.
• 3. Lowpass spatial filtering
• (1) Mask for 3?3 neighborhood

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4.3.2Smoothing Filters(2)

• (2) Operation -- replace z5 by
• (3) Also called neighborhood averaging
• (4) See Fig. 4.22 for effect
• 4. Median filtering
• (1) Reducing noise without blurring images

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4.3.2Smoothing Filters(3)

• (2) Operation --
• replace g. l. at (x, y) with the median of all
  the g. l. of neighborhood.
• (3) Meaning of median
• value r such that
• (i.e., r (1/2)tile of the p.d.f. )

P(x)
r median
x
Area 1/2
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4.3.2Smoothing Filters(4)

• (4) An example
• given
• g. l. z5 15 is replaced by median 20
• (5) For effect of median filtering, see Fig. 4.23

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4.3.3Sharpening Filters(1)

• 1. Objective
• highlighting or enhancing fine details in images.
  
• 2. Applications
• (1) electronic printing
• (2) medical imaging
• (3)industrial inspection
• (4) target detection
• etc.

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4.3.3Sharpening Filters(2)

• 3. Basic highpass spatial filtering (HPSF)
• (1) Mask for 3?3 neighborhood
• (2) See Fig. 4.25 for effect of filtering
• 4. High best filtering
• (1) Also called high-frequency emphasis
  filtering.

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4.3.3Sharpening Filters(3)

• (2) Method
• high-best A ? (original) - lowpass
• (A-1)(original) original - lowpass
• (A-1)(original) highpass
• where A is a selected weight.
• (3) Note that part of the original image is added
  back.
• (4) Equivalent mask
• (5) See Fig. 4.27 (A1.1 is enough)

Where w9A-1 (A 1 ? basic HPSF)
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4.3.3Sharpening Filters(4)

• 5. Derivative filters
• (1) Concept -
• (2) The most common differentiation operation is
  the gradient

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4.3.3Sharpening Filters(5)

• (3) Gradient
• a. definition -- the gradient of a function f at
  a pixel (x0, y0) is
• b. magnitude of gradient --

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4.3.3Sharpening Filters(6)

• (4) Approximation of gradient magnitude
• a. Assume the neighborhood (nbhd) g. l. of the
  pixel at (x, y) are
• b. in continuous form

With g. l. at (x, y) z5
or
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4.3.3Sharpening Filters(7)

• C. in absolute difference form
• d. Roberts operators for 2 ? 2 nbhd
• operation N ? MR1 N ? MR2 z5-z9
  z6 - z8

or
MR1
MR2
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4.3.3Sharpening Filters(8)

• d. Prewitt operators for 3 ? 3 nbhd
• operation N ? MP1 N ? MP2
• (z7z8z9) - (z1z2z3) (z3z6z9) -
  (z1z4z7)
• e. Sobel operators for 3 ? 3 nbhd
• operation N ? MS1 N ? MS2
• (z72?z8z9) - (z12?z2z3)
• (z32?z6z9) - (z12?z4z7)

MP1
MP2
MS1
MS2
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4.4 Enhancement in Frequency Domain

• 4.4.1 Lowpass Filtering
• 4.4.2 Highpass Filtering
• 4.4.3 Homomorphic Filtering

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4.4.1 Lowpass Filtering(1)

• 1. Use
• image blurring ( smoothing )
• 2. Goal
• Want to find a transfer function H(u, v) in the
  frequency domain to attenuate the high frequency
  in the FT F(u, v) of a given image f using the
  inverse FT

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4.4.1 Lowpass Filtering(2)

• 3. Ideal lowpass filter (ILPF)
• (1) Definition --
• H(u, v) 1 if D(u, v) ? D0
• 0 otherwise
• where D(u, v) distance from (0, 0) to (u, v)
• and D0 is a constant ( called cutoff frequency )
• (2) See Fig 4.30 for the filter shape in 3-D and
  2-D
• (3) The ILPF cannot be implemented by analog
  hardware ( but can be implemented by software )
• (4) Before seeing effects of the ILPF, we need to
  review more properties of the FT first.

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4.4.1 Lowpass Filtering(3)

• 4. Additional review of the Fourier transform
• See sec.3.23.4 for FT, DFT, FFT
• See Fig. 4.31 for an example of Fourier spectrum
  ( or simply called spectrum )
• 5. See Fig. 4.32 for effects of applying the ILPF
  using different cutoff frequencies.
• 6. The ILPF produces ringing effects see Fig.
  4.32(d) for an example and see Fig. 4.33 for the
  reason. Note Fig. 4.33(a) is equivalent to the
  top view of a 2-D sinc function.

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4.4.1 Lowpass Filtering(4)

• 7. Butterworth lowpass filter ( BLPF )
• (1) A BLPF of order n with cutoff frequency at D0
  is defined as
• where A 1 or 0.414
• (2) See Fig. 4.34 for the shape of the BLPF.
• (3) See Fig. 4.35 for the effects of applying the
  BLPF with n 1 for 5 D0 values.
• 8. The BLPF produces no ringing effect due to the
  smoothness of its transfer function where A1 or
  0.414

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4.4.2 Highpass Filtering(1)

• 1. Use
• Image sharpening
• 2. Ideal highpass filter (IHPF)
• (1) Transfer function
• H(u, v) 0 if D(u, v) ? D0
• 1 otherwise
• (2) See Fig. 4.37 for shapes of the IHPF.

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4.4.2 Highpass Filtering(2)

• 3.Butterworth highpass filter (BHPF)
• (1) Transfer function
• where A 1 or 0.414
• (2) See Fig. 4.38 for shapes of the BHPF.
• 4.4.3 Homomorphic Filtering
• 4.5 Generation of spatial masks from frequency
  domain specifications
• Read the textbook

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4.6Color Image Processing

• 4.6.0 Introduction
• 4.6.1 Color fundamentals
• 4.6.2 Color models
• 4.6.3 Pseudo-color image processing
• 4.6.4 Full color image processing

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4.6.0Introduction

• 1. Motivation
• (1) Color is a powerful descriptor for automated
  image analysis.
• (2) The human eye can discern thousands of color
  shades and intensities ( but about only a dozen
  of grey levels )
• 2. Study areas
• (1) full color image processing
• still in infancy
• (2) Pseudo - color image processing
• assigning color shades to monochrome intensity
  images

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4.6.1Color Fundamentals(1)

• 1. Colors of light
• (1) Primary -- red (R), green (G), and blue (B)
• (2) Secondary -- magenta (RB),
• cyan (GB)
• yellow (RG)
• (3) See plate III(a) for illustration.
• 2. Colors of pigments (colorants) --
• (1) Primary -- magenta, cyan, and yellow
• (2) Secondary -- red, green, and blue
• (3) See plate III(b) for illustration.

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4.6.1Color Fundamentals(2)

• 3. Characteristics of color
• (1) Three basic characteristics
• a. brightness -- chromatic notion of intensity
• b. hue -- dominant wavelength (color) perceived
  by human eyes
• c. saturation -- amount of white light mixed with
  hue
• (2) Chromaticity -- hue saturation
• (3) trimulus values
• amounts of red, green, and blue (denoted as X, Y,
  and Z, respectively ) for a color

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4.6.1Color Fundamentals(2)

• (4) trimulus coefficients -- x, y, z, with
• x X / (X Y Z)
• y Y / (X Y Z)
• z Z / (X Y Z)
• (5) Chromaticity diagram -- Plate IV

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4.6.2Color models(1)

• 1. Models
• (1) RGB (red, green, blue ) model
• useful for hardware e. g., color monitors, TV
  cameras, etc
• (2) CMY ( cyan, magenta, yellow ) model
• useful for color printers
• (3) YIQ ( luminance, inphase, quatrature ) model
• useful for color TV broadcasting
• (4) HSI (hue, saturation, intensity ) model
• useful for color image manipulation
• (5) HSV (hue, saturation, value ) model
• useful for color image manipulation

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4.6.2Color models(2)

• 2. Models most frequently used in image
  processing
• RGB, YIQ, HIS
• 3. RGB model
• (1) Good for analysis of aerial satellite
  multispectral image data ( including 4 images of
  G, R and two infrared ).
• (2) No good for natural scene image processing if
  R, G, B are treated separately ( e. g., human
  face processing ).
• (3) See Fig. 4.44 for RGB color cube.

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4.6.2Color models(3)

• 4. YIQ model
• (1) Y represents the luminance component.
• (2) Y and color information ( i.e., I Q ) are
  decoupled.
• (3) Contrast enhancement of an image in the YIQ
  model can be achieved by applying histogram
  equalization to the Y component only.
• 5. HSI model
• (1) I represents intensity.
• (2) advantages
• a. I and color information ( i.e., H S ) are
  decoupled

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4.6.2Color models(4)

• b. color information represented by H S is
  close to the color observed by eyes.
• (3) Good for human color inspection works.
• 6. Model conversions
• (1) RGB ? YIQ -- use Eq. 4.6-6
• (2) RGB ? HSI -- use Eq. 4.6-11, 18, 21 for I, H,
  S
• (3) HSI ? RGB -- for detail, see pp 236-237 of
  the textbook.

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4.6.3 Pseudo - color image processing(1)

• 1. Purpose
• to assign color to monochrome images based on
  properties of gray - level content of images.
• 2. Method
• (1) Intensity slicing
• (2) Gray level to color transformation
• (3) Filtering
• 3. Intensity slicing
• (1) slicing into two colors means the following
  transformation

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4.6.3 Pseudo - color image processing(2)

• (2) General slicing means the following
  transformation

Color
cM
c2
c1
L
I1
I2
IM
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4.6.3 Pseudo - color image processing(3)

• 4. Gray level to color transformation
• (1) More general than intensity slicing.
• (2) Method
• feed image gray level into three (RGB)
  independent transformation functions and display
  the results in a color monitor ( see Fig. 4.50
  for illustration )
• (3) For example, see Fig. 4.51 and Plate VI.
• (4) Advantages
• specific details in images may be emphasized.

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4.6.3 Pseudo - color image processing(4)

• 5. A filtering approach
• (1) The principle is the same as that of gray
  level to color transformation except that the
  transformation are performed in the frequency
  domain.
• (2) See Fig. 4.52 for illustration.
• (3) Various forms of bandreject filters are used
  here ( see the textbook

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4.64 Full Color Image Processing

• 1. Only color image enhancement is discussed
  here.
• 2. When the HIS model is used, intensity is
  decoupled from color information. So, we can
  enhance the I component using any enhancement
  technique for monochrome images.
• 3.Detail procedure when the RGB model is used
• RGB HSI HIS RGB
• 4. See Plate IX for an example.